Historically, many researchers have relied, and currently rely, on joint normality (e.g., [1]}, [2]}, [3]}). Critical adjustments ate often done with recursive sub-density estimation; see [4]}. Section REF  places Armitage's sub-density formula in the broader probability framework of possible events and confirms, from the prospective of this \(\sigma \) -algebra, that the common current practice of using Armitage's formula for calculating distributions of interim test statistics is appropriate.
